This invention relates to a method of evaluating the imaging performance of an imaging optical system. More particularly, the invention is concerned with an imaging performance evaluating method for use in performance inspection of an imaging optical system in a registration inspecting apparatus, for example, which is useable for inspection of an optical performance such as distortion or alignment precision, of a projection optical system in a semiconductor device manufacturing exposure apparatus of step-and-repeat type or step-and-scan type, for example.
In projection exposure apparatuses for the manufacture of semiconductor devices, a performance for printing, through projection exposure, a circuit pattern of a reticle onto a wafer with high resolution is required to meet further increases in density of an integrated circuit. In an attempt to improve the resolving power for the projection of a circle pattern, a method in which the numerical aperture (NA) of a projection optical system is enlarged while keeping the wavelength of exposure light fixed, a method of shortening the wavelength of exposure light (e.g., changing from g-line to i-line, from i-line to the emission wavelength of an excimer laser or to that of an F2 laser, or a method using SOR light), have been proposed and developed.
On the other hand, in the stream of further miniaturization of a circuit pattern, a performance for aligning a wafer and a reticle having an electronic circuit pattern formed thereon very precisely, is also required. Generally, the required alignment precision is about one-third or less of the linewidth of a circuit pattern. For a 1G bit DRAM, for example, if the circuit pattern is based on 0.18 micron rule, an overlay precision (alignment through the whole exposure region) of 60 nm or less is required.
Further, in a registration inspecting apparatus wherein this overlay precision is measured, a precision of about one-tenth of the overlay precision is required. For a 1G bit DRAM, a precision of 6 nm or less is necessary.
For higher precision measurement in such registration inspecting apparatuses, a method called a TIS (Tool Induced Shift) correction method wherein the influence of TIS, which is a detecting system factor among the measurement error producing factors, is reduced, has been proposed and developed.
FIG. 1A is a schematic view for explaining this TIS correction method. FIG. 1A shows an example wherein a surface step (difference in level) is defined on a silicon wafer 1 by an etching process, and wherein the relationship between an etching pattern (first mark) 2 based on the level difference and a resist image pattern (second mark) 3 having been printed and developed after the alignment process is going to be measured. In accordance with the TIS correction method, the measurement is made twice. Here, the second time measurement is performed while rotating the wafer 1 by 180 degrees as compared with the first time measurement. The result of such a first time measurement is called xe2x80x9c0-deg. measured valuexe2x80x9d (xcex940-deg), and the result of a second time measurement is called xe2x80x9c180-deg. measured valuexe2x80x9d (xcex94180-deg). In the TIS correction method, a value obtainable by dividing, by 2, the difference of a 0-deg. measured value minus a 180-deg. measured value, is used as a measured value. On the basis of this, an error in the detection system factor is reduced, whereby high precision measurement can be accomplished. Here, the value obtainable by dividing, by 2, the sum of the 0-deg. measured value plus the 180-deg. measured value, is called xe2x80x9cTISxe2x80x9d.
Use of such a TIS correction method will be effective to reduce the measurement error of the detection system factor. However, it is still insufficient. For example, even if one and the same wafer is measured in accordance with the TIS correction method by using two different measuring machines, there may occur a large difference, as shown in FIG. 1B. As regards this alignment precision, since the alignment sequence of the exposure apparatus is based on the global alignment method, it does not become worse beyond xe2x80x9croot 2xe2x80x9d times the precision of a stage system of the exposure apparatus, having an interferometer and for driving the wafer.
The result of the measurement by the registration inspecting apparatus #2 of FIG. 1B is, however, worse by much more than xe2x80x9croot 2xe2x80x9d times the precision of the stage system for driving the wafer and having an interferometer. Thus, clearly, it is attributable to a factor in the registration inspecting apparatus.
This results from the TIS-WIS interaction on an occasion when there is a WIS (Wafer Induced Shift), which is a wafer factor among the measurement error producing factors. In this example, the insufficiency of the result based on the TIS correction is clearly seen in FIG. 1B. New semiconductor processes such as a Cu-CMP process, for example, will be introduced successively and, in those cases, there will still be WIS present. In consideration of this, for improvement in precision of a registration inspecting apparatus, it is desirable that the TIS be removed as much as possible to thereby prevent the TIS-WIS interaction.
In the TIS correction method, the measurement has to be done twice, at 0 degree and 180 degree. This is a large problem in relation to the throughput. In current mass-production of semiconductor devices, therefore, the TIS correction method is not used prevalently.
As regards removal of TIS, the cause of production of TIS due to an optical factor as well as conventional examples therefor will be described. Most of currently used registration inspecting apparatuses or alignment detecting systems are based on a bright-field image processing process.
FIG. 2 is a schematic view of an example of a registration inspecting apparatus. In this example, a special mark (first and second marks 2 and 3) is provided on a wafer 1, and an image of the mark is formed through an optical system upon an image pickup device such as a CCD, for example. An electric signal therefrom is processed, by which the positions of the first and second marks 2 and 3 are detected. The imaging performance which is most necessary in this optical system is the symmetry of images corresponding to the first and second marks 2 and 3. If there is something in the optical system (imaging optical system) that deteriorates the image symmetry, it means that there is TIS present.
In these types of alignment detecting systems, the magnification is made high (e.g., about 100xc3x97) and, in most cases, it is used on or in the proximity of the axis. For this reason, the major cause for deterioration of symmetry of the mark image is not an off-axis aberration but an eccentric coma aberration close to the axis of the optical system and the non-uniformness in an illumination system.
Further, it has been found that the symmetry of a mark image changes with the amount of surface level difference (height of a surface-step) upon a wafer to be measured.
FIG. 1C is a schematic view for explaining a first mark 2 and a second mark 3 formed on the wafer 1 of FIG. 2, and it illustrates the manner of calculating the symmetry SOI (Symmetry of Image) to be produced by a signal (waveform intensity) which is based on the first and second marks 2 and 3.
When the waveform intensities at the opposite ends 2a and 2b of the first mark 2 are denoted by a and b, respectively, and when the waveform intensity based on the wafer top surface is denoted by c, the symmetry SOI can be determined in accordance with:
SOI=100(axe2x88x92b)/c. 
FIG. 1D shows the results of the symmetry SOI of the optical image as defined with reference to FIG. 1C, which were obtained experimentally while changing the amount of surface level difference SH. In the experiments, the symmetry SOI of the image was measured while taking the eccentric coma aberration of the optical system as xcex/4 and xe2x88x92xcex/20 (where xcex is the illumination wavelength).
As seen from FIG. 1D, the symmetry SOI of the optical image changes relative to the surface level difference SH in accordance with a sine function of the period xcex/2 (where xcex is the illumination wavelength), and the amplitude thereof is dependent upon the coma aberration of the optical system. Further, it has been found that, in relation to the non-uniformness of the illumination system, too, the symmetry changes in accordance with a sine function of the same period, and that the amplitude is dependent upon the non-uniformness of the illumination system. Furthermore, this phenomenon has been confirmed not only by experiments but also by simulations or analyses based on models.
When the measurement is made on the basis of reflection, as shown in FIG. 1D, the asymmetry of the optical image becomes largest with a surface level difference corresponding to a multiple of xe2x85x9 of the illumination wavelength xcex by an odd number, that is, xcex/8 or 3xcex/8, for example. On the other hand, with a surface level difference corresponding to a multiple of xe2x85x9 of the illumination wavelength by an even number, that is, 2xcex/8 or 4xcex/8, for example, the symmetry of the optical image can be held independently of the coma aberration or non-uniformness of the illumination system. In other words, there are a surface level difference which is sensitive to the coma aberration or non-uniformness of the illumination system and a surface level difference which is not sensitive to them.
In consideration of the above, an evaluation method which uses such a sensitive surface level difference, for high precision evaluation of the coma aberration of an optical system and non-uniformness of the illumination system, has been proposed in Japanese Laid-Open Patent Application, Laid-Open No. 9-280816, filed by the assignee of the subject application.
Here, this evaluation method will be called a xe2x80x9ctwo-mark interval measurement method TIS2xe2x80x9d. FIG. 1E illustrates the same. As the surface level difference of these two marks D1 and D2, values of xcexc/8 and 3xcexc/8 (or multiples of them) are used. While the foregoing description has been made with reference to monochromatic illumination light xcex having no illumination wavelength bandwidth, in the discussion below, the description will be made with reference to the use of illumination light having a certain bandwidth. Thus, xcexc denotes the center wavelength of the illumination light to be used in an alignment optical system and having a certain bandwidth.
The amounts of surface level differences xcexc/8 and 3xcexc/8 are those values both of which reflect the coma aberration of the optical system and non-uniformness of the illumination system, sensitively. The asymmetry of them lies in opposite directions, and also the influence of it to the measured value, in the marks D1 and D2 (values of the marks D1 and D2 are positive), is produced in the opposite directions, as shown in FIG. 1E.
Since the orientation of the marks D1 and D2 is unchanged with the rotation of the wafer by 180 degrees, a half of the difference between the measured values at the 0-deg. and the 180-deg. corresponds to the sum TIS2 of the marks D1 and D2. Thus, the measurement can be done with double sensitivity, as compared with a case where only one surface level difference is used.
Next, the results of practical application of this evaluation method will be described. First, the two-mark interval measurement TIS2, which is the item of evaluation, was applied to an alignment optical system for use in an alignment process in a semiconductor device manufacturing exposure apparatus, which optical system is substantially equivalent to the optical system shown in FIG. 2, and investigations were made with respect to the correspondence of it. FIGS. 1F and 1G show the relation with respect to the two-mark interval measurement TIS2, with a portion of the alignment optical system being changed to change the eccentric coma aberration and non-uniformness of the illumination system.
In both of FIGS. 1F and 1G, it is seen that both have a correlation with TIS2. The evaluation method based on two-mark interval measurement needs the use of two surface level differences which are sensitive and which have asymmetry in opposite directions. While it depends on the size of the mark, if the two surface level differences are not covered by the measurement range simultaneously, the measurement has to be done in cooperation with motion in the measurement direction. As described hereinbefore, the surface level differences of the marks to be used in the two-mark interval measurement TIS2, those corresponding to xe2x85x9 and xe2x85x9c with respect to the center wavelength xcexc of the illumination light to be used in the alignment optical system, that is xcexc/8 and 3xcexc/8, are used.
Although there is an effect obtainable with the use of these surface level differences, in an exact sense, taking it with reference to the center wavelength xcexc of the illumination light is still insufficient. In a registration inspecting apparatus for which a precision of one-tenth or less of the overlay precision is required, an evaluation criterion should be prepared while taking into account any other variables.
It is an object of the present invention to provide an evaluation method by which an imaging performance of an imaging optical system can be evaluated, with a high sensitivity.